In recent years, cardiac dysfunction has become the most common cause of death in the western world. Advances in imaging science and, more recently, computational physiology provide significant potential to circumvent many of the current limitations in diagnosis and therapy planning. A key element to the application of these technologies is the extraction of clinically relevant information from patient data.
To date, fluid mechanics models have been widely used to analyse cardiovascular blood flow and more recently been integrated with tissue mechanics to understand coupled cardiac function. The fluid domain behaviour has been evaluated based on numerical discretisation techniques. The flow domain has also been coupled numerically to solid mechanics models based on monolithic or even mixed approaches. In these models, both the intra-ventricular pressure and velocity fields are a direct consequence of the continuum mechanics principles of mass and momentum conservation as well as the imposed boundary conditions. These boundary conditions are the pressures on the inside surfaces of the heart chamber and vessel walls. The problem therefore, with these methods, is that boundary conditions must be imposed which leads to inaccurate calculation of the flow fields.
An alternative to calculating flow fields from pressure boundary conditions is to determine pressure from known flow fields. In this case the so-called Pressure Poisson Equation (PPE) can be derived directly from the well-known Navier-Stokes equations. This pressure information is in turn very valuable for the formulation of more realistic boundary conditions for the models described above. For example, the PPE has been used to determine relative pressure fields from a sequence of ultrafast cardiac Comupted Tomography (CT) images.
Ongoing clinical research has established phase contrast magnetic resonance velocity mapping as a useful tool to gain non-invasive insight into dynamic cardiovascular blood flow in a wide range of contexts. Of course, other imaging tools may also be used, such as ultrasound.
A similar approach as that used for the analysis of CT images, as described above, has been applied for the computation of flow pressure fields from MR velocity mapping. Their applied mathematical formulation is based on the assumption that the contribution of viscous terms to the pressure calculation can be neglected which holds true only for high Reynolds number flow. Furthermore, the underlying numerical discretisation requires an iterative solution in order to determine unknown boundary conditions. The need for applying these boundary conditions on the fluid domain further complicates the direct use of the actual imaging space as computational domain. As an alternative, multi-directional intra-cardiac flow relative to selected planes has been analysed, as well as the flow relative to volumes of acquisition. However, again these methods require an iterative solution to determine unknown boundary conditions.
It is, therefore, an object of the present invention to provide a method of computation of intra-vascular differences of pressure, directly from the velocity data.